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Chapter 1: Problem 51

Rewrite each angle in degree measure. (Do not use a calculator.) (a) \(\frac{3 \pi}{2}\) (b) \(\frac{7 \pi}{6}\)

Short Answer

Expert verified
The angle \(\frac{3 \pi}{2}\) in degree measure is 270掳 and the angle \(\frac{7 \pi}{6}\) in degree measure is 210掳.

Step by step solution

01

Recall the Conversion Formula

Remember that \( \pi \) radians is equal to 180 degrees. We will use this knowledge to convert the given radian measures to degrees.
02

Convert \(\frac{3 \pi}{2}\) to Degree Measure

In order to convert \(\frac{3 \pi}{2}\) radians to degrees, cross-multiply by the equivalent degree value of \( \pi \) which is 180. Thus, \(\frac{3 \pi}{2}\) radians = \(\frac{3 \pi}{2}\) * 180掳/\( \pi \). The \( \pi \) will cancel out, leaving \( \frac{3}{2}\) * 180掳. Simplify this to get 270掳.
03

Convert \(\frac{7 \pi}{6}\) to Degree Measure

To convert \(\frac{7 \pi}{6}\) radians to degrees, cross-multiply by the equivalent degree value of \( \pi \), which is 180. Thus, \(\frac{7 \pi}{6}\) radians = \(\frac{7 \pi}{6}\) * 180掳/\( \pi \). The \( \pi \) will cancel out, leaving \( \frac{7}{6}\) * 180掳. Simplify this to get 210掳.

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